This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
-Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013.
Other Sources
-K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.
Course Schedules
Week
Contents
Learning Methods
1. Week
Review of Calculus, Taylor Polynomial
Lectures and recitation
2. Week
Round-off Errors, Computer Arithmetic and Rate of Convergence
Lectures and recitation
3. Week
The Bisection Method, Fixed-Point Iteration
Lectures and recitation
4. Week
Newton’s Method, Secant Method,False Position Method
Romberg Integration, Elementary Theory of Initial-Value Problems Euler’s Method
Lectures and recitation
13. Week
Modified Euler, Heun and Runge-Kutta of Order 4 Methods
Lectures and recitation
14. Week
Iterative Methods for the Solution of Systems of Linear Equations
Lectures and recitation
15. Week
Final week
Exams
16. Week
Final week
Exams
17. Week
Final week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Final Exam
1
60
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems.
PO-2
Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex systemi process, device or product under realistic constraints and conditions, in such a way as to meet the desired results; ability to apply modern design methods for this purpose.
PO-4
Ability to select and use modern techniques and tools needed for analyzing and Solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectivley, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instruction.
PO-8
Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9
Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO-10
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO-11
Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
Understand IEEE standard binary floating point format, machine precision and computer errors
LO-2
Develop understanding of the Talyor series to set up approximate polynomials.
LO-3
Use the bisection method to solve the equation f(x)=0 and estimate the number of iterations in the algorithm to achieve desired accuracy with the given tolerance
LO-4
Use the iterative method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps.
LO-5
Use Newton's method or the Secant method to solve the equation f(x)=0 within the given tolerance.
LO-6
Use polynomial interpolations, including the Lagrange polynomial for curve fitting, or data analysis; use Neville's iterative algorithm, Newton's divided difference algorithms to evaluate the interpolations.
LO-7
Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations.
LO-8
Use the open or closed Newton-Cotes formula, including the Trapezoidal rule and Simpson's rule, to approximate definite integrals; use the Lagrange polynomial to estimate the degree of accuracy; derive the composite numerical integration using the open or closed Newton-Cotes formula.
